The present applicant has already proposed an internal combustion engine in which a lean air-fuel mixture is burned, in which internal combustion engine an NO.sub.x absorbent which absorbs the NO.sub.x when the air-fuel ratio of an inflowing exhaust gas is lean and releases the absorbed NO.sub.x when the oxygen concentration in the inflowing exhaust gas is lowered is arranged in an engine exhaust passage; the NO.sub.x generated when the lean air-fuel mixture is burned is absorbed by the NO.sub.x absorbent before the NO.sub.x absorption capability of the NO.sub.x absorbent is saturated, the air-fuel ratio of the inflowing exhaust gas to the NO.sub.x absorbent is temporarily made rich so that the NO.sub.x absorbent is made to release the NO.sub.x and, at the same time, the released NO.sub.x is reduced (refer to U.S. patent application Ser. No. 08/066,100 or European Patent Application No. 92920904.7).
However, the fuel and the lubrication oil of the engine contain sulfur, and therefore SO.sub.x is contained in the exhaust gas. Accordingly, in this internal combustion engine, this SO.sub.x is also absorbed into the NO.sub.x absorbent together with the NO.sub.x. However, this SO.sub.x is not released from the NO.sub.x absorbent even if the air-fuel ratio of the inflowing exhaust gas to the NO.sub.x absorbent is made rich, and accordingly the amount of SO.sub.x in the NO.sub.x absorbent is gradually increased. However, when the amount of SO.sub.x in the NO.sub.x absorbent is increased, the amount of the NO.sub.x that can be absorbed by the NO.sub.x absorbent is gradually lowered, and finally the NO.sub.x absorbent becomes no longer able to absorb almost any NO.sub.x. Therefore, the present applicant has already proposed an internal combustion engine in which a sulfur trap is provided in the engine exhaust passage at the upstream side of the NO.sub.x absorbent, and the SO.sub.x contained in the exhaust gas is caught by this sulfur trap (refer to U.S. patent application Ser. No. 08/096,103 or European Patent Application No. 93112260.6). In this internal combustion engine, the SO.sub.x discharged from the engine is caught by the sulfur trap, and therefore only the NO.sub.x is absorbed into the NO.sub.x absorbent.
However, in this internal combustion engine, the SO.sub.x caught by the sulfur trap is continuously being caught in the sulfur trap without being released from the sulfur trap even if the air-fuel ratio of the exhaust gas flowing into the sulfur trap is made rich. Accordingly, the amount of the SO.sub.x caught by the sulfur trap is gradually increased. When the SO.sub.x catching capability of the sulfur trap is saturated, the SO.sub.x passes through the sulfur trap, and therefore there arises a problem in that the SO.sub.x is absorbed into the NO.sub.x absorbent and gradually accumulates in the NO.sub.x absorbent.